Coupling quantized spin waves (magnons) with quantized lattice vibrations (phonons) reveals great promise towards coherent quantum information processing. To achieve this, phonons must become trapped inside a yttrium-iron-garnet (YIG) crystal that encourages resonance of a specific phonon mode, so magnons can match this resonance frequency to initiate coupling. Current methods use high-overtone bulk acoustic wave resonances (HBARs) which enables multiple phonon modes to simultaneously resonate inside YIG, increasing the rate of coupling. However, these methods use a rectangular YIG to produce HBAR phonons which suffer diffraction losses in rectangular resonating cavities, limiting the coupling strength. Our research focuses on trapping shear modes of phonons in confocal shaped HBAR (cHBAR) resonators since recent cavity optomechanical studies revealed this improves the lifetime and quality of trapped longitudinal phonon modes. To achieve this same result with shear cHBAR phonon modes we will use elastic wave theory to analytically obtain the YIG shape needed to produce them. This research not only shines a light on previously unexplored shear cHBAR phonon modes, but is expected to directly improve magnon-phonon coupling, thereby promising an efficient operation of YIG for quantum information applications.